(5 marks) nver of charge carriers contained in 12cmtimes 10mmtimes 0.5m of the new material (2 marks) 2.Starting from the mechanical equation of motion of electron inside a superconductor, show that the rate of change current density is directly dependent on the electric field vector. 3.A Hall probe consists of copper strip, n=8.5times 10^28m^-3 and of cross-sectional Determine the magnetic field (6 marks)

To determine the number of charge carriers contained in the given material, we need to calculate the volume of the material and then multiply it by the number of charge carriers per unit volume.<br /><br />Given:<br />Length of the material = 12 cm<br />Width of the material = 10 mm = 0.1 cm<br />Height of the material = 0.5 m = 50 cm<br /><br />Volume of the material = Length × Width × Height<br />Volume of the material = 12 cm × 0.1 cm × 50 cm = 60 cm³<br /><br />Number of charge carriers per unit volume = n<br />Number of charge carriers = n × Volume of the material<br />Number of charge carriers = 8.5 × 10²⁸ m⁻³ × 60 × 10⁻⁶ m³ = 5.1 × 10²²<br /><br />Therefore, the number of charge carriers contained in the given material is 5.1 × 10²².<br /><br />To show that the rate of change of current density is directly dependent on the electric field vector, we can start with the mechanical equation of motion of an electron inside a superconductor.<br /><br />The equation of motion for an electron in a superconductor is given by:<br /><br />m * a * E<br /><br />where m is the mass of the electron, a is the acceleration of the electron, e is the charge of the electron, and E is the electric field vector.<br /><br />Rearranging the equation, we have:<br /><br />a = (e * E) / m<br /><br />The acceleration of the electron is directly proportional to the electric field vector. Now, let's consider the current density (J) and its rate of change.<br /><br />Current density (J) is defined as the current (I) per unit area (A):<br /><br />J = I / A<br /><br />The rate of change of current density (dJ/dt) is related to the acceleration of the electron. Since the acceleration is directly proportional to the electric field, the rate of change of current density is also directly dependent on the electric field vector.<br /><br />For the Hall probe, we need to determine the magnetic field using the Hall effect. The Hall voltage (V_H) is given by:<br /><br />V_H = -R_H * I / A * B<br /><br />where R_H is the Hall coefficient, I is the current flowing through the strip, A is the cross-sectional area of the strip, and B is the magnetic field.<br /><br />Given:<br />n = 8.5 × 10²⁸ m⁻³<br />Width of the strip = w<br />Thickness of the strip = t<br /><br />The Hall coefficient (R_H) is given by:<br /><br />R_H = 1 / (ne)<br /><br />The current (I) flowing through the strip is:<br /><br />I = n * e * v * w * t<br /><br />The cross-sectional area (A) of the strip is:<br /><br />A = w * t<br /><br />Substituting these values into the Hall voltage equation, we get:<br /><br />V_H = -1 / (ne) * n * e * v * w * t * B / (w * t)<br /><br />Simplifying, we have:<br /><br />V_H = -v * B<br /><br />Therefore, the magnetic field (B) can be determined as:<br /><br />B = -V_H / v<br /><br />Hence, the magnetic field can be determined using the Hall effect with the given values.